1. What is the test statistic? What is the p-value?
2. At a 5% significance level (95% confidence level), what is the critical value(s) in this test? Do we reject the null hypothesis?
3. What are the border values of x between acceptance and rejection of this hypothesis?
4. Given a fair, six-sided die, what is the probability of rolling the die twice and getting a"1" each time?
5. What is the probability of getting "1" on the second roll when you get a "1" on the first roll?
6. The house managed to load the die in such a way that the faces "2" and "4" show up twice as frequently as all other faces. Meanwhile all other docs will show up with equal frequency. What twice is the probability of getting a "5" when rolling this loaded die?
7. Write the probability distribution for this loaded die, showing each outcome and its probability.
8. Determine SSxx=,SSxy=and SSyy=
9. Find the equation of the regression line. What is the predicted value when x =4 ?
A group of students from three universities were asked to pick their favorite college sport to attend of their choice: The results,in number of students,are listed as follows:
|
|
Football
|
Basketball
|
Soccer
|
|
Maryland
|
60
|
70
|
20
|
|
Duke
|
10
|
75
|
15
|
|
|
|
|
10. What is the probability that the student is from UCLA or chooses football?
11. What is the probability that the student is from Duke, given that the student chooses basketball?
12. What is the probability that the student is from Maryland and chooses soccer?
13. How many mangoes have weights between 14 ounces and 16 ounces?
14. What is the probability that a randomly selected mango weighs less than 14 ounces?
15. A quality inspector randomly selected 100 mangoes from the shipment.
a. What is the probability that the 100 randomly selected mangoes have a mean weight less than 14 ounces?
b. Do you come up with the same result in Question 14? Why or why not?
16. Suppose that in a box of 20 iPhone devices, there are 5 with defective antennas. In a
draw without replacement, if 3 iPhone devices are picked, what is the probability that all 3 have defective antennas?
Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way shown in the following table.
|
Leading digit
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
|
Distr of leading digit
|
30.1
|
17.6
|
12.5
|
9.7
|
7.9
|
6.7
|
5.8
|
5.1
|
4.6
|
The owner of a small business would like to audit its account payable over the past year because of a suspicion of fraudulent activities. He suspects that one of his managers is issuing checks to non-existing vendors in order to pocket the money. There have been 790 checks written out to vendors by this manager. The leading digits of these checks are listed as follow: 50, 15, 12, 74, 426, 170, 11, 23, 9
17. Suppose you are hired as a forensic accountant by the owner of this small business, what statistical test would you employ to determine if there is fraud committed in the issuing of checks? What is the test statistic in this case?
18. What is the critical value for this test at the 5% significance level (95% confidence level)? Do the data provide sufficient evidence to conclude that there is fraud committed?